I'm using a lm2596 buck converter, tuned to exatcly 5.00v but when i measure the 5v pin, it is at 4.8v and the screen shows that under voltage indicator.
Should I increase the input voltage until the pin 4 (5v) reaches... uh... 5v?
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The acceptable input voltage range is 5V ±5%. See Raspberry Pi Power Limitations
Many power supplies are actually designed to output more than 5V to compensate for cable loss. You are extremely unlikely to cause any damage. The Pi itself is actually tolerant of slightly higher voltage; the Pi3 does not actually run off 5V, and has an on-board regulator to supply the SOC. In fact the Pi itself will run at lower voltages, although this may affect peripherals.
The 5V is used mainly for peripherals (HDMI, USB peripherals).
Yes, that should be fine - I'm doing something similar myself and it helps to compensate for the voltage-drop across the fraction of an ohm resistance the F1 "poly-fuse" has (which is in series with the power input before it goes to the rest of the RPi circuitry).
There is one proviso though: you should trim the supply so the 5v pin is at the desired value (e.g. 5.0V or slightly above) with as much of anything that is attached to the GPIO 26/40 pin connector disconnected and any USB equipment that might not always be attached not being attached.
This is because the voltage drop across F1 will vary in proportion to the current through it (in accordance with Ohms law provided the current is not so high that it starts to heat up and the resistance increases and it makes more heat and the resistance increases etc. in a positive feed-back way) and you want to adjust your supply when the current is at a minimum and thus the voltage drop is also at a minimum so the "adjusted" voltage on pins 4 (and 2) is as high as it will get.
As you might imagine if you tweak the voltage on pin 4 to the upper level (5.25V anyone) under maximum loading, when you remove some of the loading, e.g. by unplugging a USB device, the current through and the voltage drop across F1 decreases and the voltage downstream of it - to the rest of the RPi circuitry and pin 4 will rise and then would go above the maximum...